Bridge Builder: Free Truss Bridge Simulator and Calculator

Free bridge simulator and truss calculator: draw a bridge from steel, timber, cables and concrete or start from Warren, Pratt, Howe, K, arch, cable-stayed and suspension designs, see every member's force and buckling check, auto-size it to the cheapest safe design, then drive cars, buses and trucks over it, blow wind across it and shake it with an earthquake.

Draw a bridge out of steel, timber, cables and concrete, then drive traffic over it, blow wind across it and shake it with an earthquake. Every member is checked for pulling and buckling, and the cost is counted as you build. Can you find the cheapest bridge that still holds?

The site Gap to cross (span): Depth of the gorge to the river bed:

Joints you put on the banks, the cliff faces or the river bed become anchors (foundations). A bank anchor costs , one in the river .

Start from a design Type Height: Panels:

auto-size it

How to build

Build (✏️): press on a joint or anywhere and drag; let go to make a member. Joints snap to a 0.5 m grid (hold Shift to place freely). The dashed circle shows the longest piece of that material.
The road must reach from one bank to the other: use a road material (dark steel or timber deck) for it. Cars only drive on road members.
Joints are pins, like a real truss: a member can only pull or push. A road on its own folds up, so brace it with triangles.
Move (✋) drags joints, Select (👆) shows a member's force and lets you change it, Delete removes. Two fingers, the right mouse button or Space + drag pans; Ctrl + wheel or pinch zooms.
Keys: B M S D tools, 1-6 materials, [ ] size, Ctrl+Z undo, Space runs the test, F fits the view.

How bridges hold up: trusses, tension and compression

A bridge has one job: carry its own weight and the traffic on it to the ground at the ends. A truss does it with straight members joined at pins. Each member can only pull (tension) or push (compression); it is never asked to bend. That is why trusses are made of triangles: a triangle cannot change shape without one of its sides getting longer or shorter, while a square can fold flat. Draw a road on its own between the banks and the simulator marks the loose joint in red: with pins, it folds.

member force and stiffness$\displaystyle N = \frac{EA}{L}\,\Delta L, \qquad \sigma = \frac{N}{A}$

buckling (Euler, combined with crushing by Rankine)$\displaystyle P_{cr} = \frac{\pi^2 E I}{L^2}, \qquad \frac{1}{P_c} = \frac{1}{f_c A} + \frac{1}{P_{cr}}$

the whole truss$\displaystyle \mathbf{K}\,\mathbf{u} = \mathbf{F}, \qquad \mathbf{K} = \sum_{\text{members}} \frac{EA}{L}\begin{bmatrix} \mathbf{c}\mathbf{c}^{T} & -\mathbf{c}\mathbf{c}^{T} \\ -\mathbf{c}\mathbf{c}^{T} & \mathbf{c}\mathbf{c}^{T}\end{bmatrix}$

chord force of a simple truss (uniform load w, span L, height h)$\displaystyle N_{\text{chord}} \approx \frac{w L^2}{8 h}$

natural frequencies and vortex shedding$\displaystyle \mathbf{K}\boldsymbol{\phi} = \omega^2 \mathbf{M}\boldsymbol{\phi}, \qquad f_s = \frac{\mathrm{St}\, U}{D}$

The last-but-one formula is the key to cheap bridges: the force in the top and bottom chords falls as the truss gets deeper, so the chords can be smaller. But the diagonals and verticals get longer, and every extra piece has to be cut, drilled, lifted and bolted. Most real steel trusses end up between about span/6 and span/10 deep. Use Find the cheapest to watch that trade-off for your own site.

The bridge types

Warren: equal triangles, diagonals alternate between tension and compression. Few pieces.
Pratt: verticals plus diagonals that slope down towards the middle, so the long diagonals are in tension and only the short verticals push. Good for steel.
Howe: the mirror image, long diagonals in compression. It suited timber, which is happy being squeezed.
K truss and Parker (camelback): shorter compression members, or a curved top chord that is deepest where the bending is biggest.
Deck truss and deck arch: the structure sits under the road, so it needs a deep gorge. An arch pushes its weight into the cliff faces, almost all in compression, which is why stone and concrete arches work.
Network tied arch: an arch above the road with crossing hangers; the road itself is the tie that holds the arch ends together.
Cable-stayed and suspension: towers and steel cables, the cheapest way past about 100 to 200 m. Cables carry huge pulls for their weight but cannot push, so the simulator lets them go slack.

What the simulator calculates

Member forces by the direct stiffness method, the same matrix method engineering software uses, for the bridge's own weight (members, a 1.5 t/m concrete deck for the steel road, joints) plus the traffic you choose. The traffic is moved across the bridge in small steps and every member keeps its worst pull and worst push (influence lines).
Strength: a member fails in tension when the stress reaches the material strength, and in compression when it buckles (Euler) or crushes, combined with the Rankine formula. The safety factor divides the strength: at 1.5 a member may only use two-thirds of it.
Auto-size is a fully stressed design: every member gets the smallest catalogue size that passes, the weight is recalculated, and it repeats until nothing changes.
Vibration: the natural frequencies and mode shapes come from the stiffness and mass matrices (subspace iteration). Cable tension adds geometric stiffness, so a suspension or cable-stayed bridge is stiffer because its cables are pulled tight.
Wind blowing across the bridge lifts the deck and sheds vortices from its edges at about f = 0.12 U / D. When that frequency is near a natural frequency the vortices lock on and the deck bounces. (The famous 1940 Tacoma Narrows collapse was a different, twisting instability called flutter; this flat side view cannot twist, and sideways wind is carried by deck bracing that is not drawn.)
Earthquakes move every anchor with a made-up ground motion: filtered random shaking with the Kanai-Tajimi spectrum (firm or soft ground), a single near-fault pulse, or a sine wave at the bridge's own frequency. The member check uses an equivalent static load: the peak ground acceleration times a design-spectrum amplification of up to 2.5 for stiff structures.
The live test is a separate time-step simulation: every joint is a mass, every member a spring with a little damping, and vehicles push down where their axles are. A member that goes past its strength snaps or buckles and is removed, and the rest of the bridge has to cope (or not).

Costs

Prices are rough 2026 figures, there to make the trade-offs real: fabricated steel about $7/kg, glulam timber $4/kg, cable $14/kg, concrete $0.80/kg (about $1,900 per cubic metre in place), a concrete deck slab $1,200 per metre, $900 per piece and $800 per joint for cutting, connections and lifting, and $12,000 per foundation on the bank or $50,000 in the river. Real projects add design, approaches, bearings, painting, traffic management and much more.

Questions

Why does my bridge say a joint can move?: A joint held by only two members in a straight line, or a rectangle without a diagonal, can swing about its pins. Add a diagonal so it becomes triangles.
Why do the cheapest designs still pass?: Auto-size checks every member against the strongest load case it sees: traffic in every position, wind up and down, and the earthquake both ways, all times the safety factor.
Why did my bridge break in the test when the check said it passed?: Moving vehicles bounce the bridge and the earthquake can resonate with it, so the forces in the test can be higher than the static ones. With a safety factor of 1 there is no margin for that.
Can I use this to design a real bridge?: No. It is a teaching model: pin joints, a flat 2D side view, typical material values and simple load cases. Real bridges are designed by licensed engineers to codes such as AASHTO, Eurocode or CSA S6, with fatigue, connections, bearings, deck bending, lateral bracing and many more checks.

Everything runs on your device and nothing is uploaded. Bending Stress & Beam Calculator · Mechanics of Materials · Brick Builder · Crash Physics · More MES tools

Comments